namespace twoDMatrixLibrary
{
	using System;

	/// <summary>
	/// Determines the eigenvalues and eigenvectors of a real square matrix.
	/// </summary>
	/// <remarks>
	/// If <c>A</c> is symmetric, then <c>A = V * D * V'</c> and <c>A = V * V'</c>
	/// where the eigenvalue matrix <c>D</c> is diagonal and the eigenvector matrix <c>V</c> is orthogonal.
	/// If <c>A</c> is not symmetric, the eigenvalue matrix <c>D</c> is block diagonal
	/// with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues,
	/// <c>lambda+i*mu</c>, in 2-by-2 blocks, <c>[lambda, mu; -mu, lambda]</c>.
	/// The columns of <c>V</c> represent the eigenvectors in the sense that <c>A * V = V * D</c>.
	/// The matrix V may be badly conditioned, or even singular, so the validity of the equation
	/// <c>A=V*D*inverse(V)</c> depends upon the condition of <c>V</c>.
	/// </remarks>
	public class EigenvalueDecomposition
	{
		private int n;           	// matrix dimension
		private double[] d, e; 		// storage of eigenvalues.
		private Matrix V; 			// storage of eigenvectors.
		private Matrix H;  			// storage of nonsymmetric Hessenberg form.
		private double[] ort;    	// storage for nonsymmetric algorithm.
		private double cdivr, cdivi;
		private bool symmetric;

		/// <summary>Construct an eigenvalue decomposition.</summary>
		public EigenvalueDecomposition(Matrix value)
		{
			if (value == null)
			{
				throw new ArgumentNullException("value");				
			}

			if (value.Rows != value.Columns) 
			{
				throw new ArgumentException("Matrix is not a square matrix.", "value");
			}
			
			n = value.Columns;
			V = new Matrix(n,n);
			d = new double[n];
			e = new double[n];
	
			// Check for symmetry.
			this.symmetric = value.Symmetric;
	
			if (this.symmetric)
			{
				for (int i = 0; i < n; i++)
				{
					for (int j = 0; j < n; j++)
					{
						V[i,j] = value[i,j];
					}
				}
		 
				// Tridiagonalize.
				this.tred2();

				// Diagonalize.
				this.tql2();
			} 
			else 
			{
				H = new Matrix(n,n);
				ort = new double[n];
					 
				for (int j = 0; j < n; j++)
				{
					for (int i = 0; i < n; i++)
					{
						H[i,j] = value[i,j];
					}
				}
		 
				// Reduce to Hessenberg form.
				this.orthes();
		 
				// Reduce Hessenberg to real Schur form.
				this.hqr2();
			}
		}
		
		private void tred2() 
		{
			// Symmetric Householder reduction to tridiagonal form.
			// This is derived from the Algol procedures tred2 by Bowdler, Martin, Reinsch, and Wilkinson, 
			// Handbook for Auto. Comp., Vol.ii-Linear Algebra, and the corresponding Fortran subroutine in EISPACK.
			for (int j = 0; j < n; j++)
				d[j] = V[n-1,j];
	
			// Householder reduction to tridiagonal form.
			for (int i = n-1; i > 0; i--) 
			{
				// Scale to avoid under/overflow.
				double scale = 0.0;
				double h = 0.0;
				for (int k = 0; k < i; k++)
					scale = scale + Math.Abs(d[k]);
				
				if (scale == 0.0) 
				{
					e[i] = d[i-1];
					for (int j = 0; j < i; j++) 
					{
						d[j] = V[i-1,j];
						V[i,j] = 0.0;
						V[j,i] = 0.0;
					}
				}
				else
				{
					// Generate Householder vector.
					for (int k = 0; k < i; k++) 
					{
						d[k] /= scale;
						h += d[k] * d[k];
					}
	
					double f = d[i-1];
					double g = Math.Sqrt(h);
					if (f > 0) g = -g;
	
					e[i] = scale * g;
					h = h - f * g;
					d[i-1] = f - g;
					for (int j = 0; j < i; j++)
						e[j] = 0.0;
		 
					// Apply similarity transformation to remaining columns.
					for (int j = 0; j < i; j++) 
					{
						f = d[j];
						V[j,i] = f;
						g = e[j] + V[j,j] * f;
						for (int k = j+1; k <= i-1; k++) 
						{
							g += V[k,j] * d[k];
							e[k] += V[k,j] * f;
						}
						e[j] = g;
					}
							
					f = 0.0;
					for (int j = 0; j < i; j++) 
					{
						e[j] /= h;
						f += e[j] * d[j];
					}
					
					double hh = f / (h + h);
					for (int j = 0; j < i; j++)
						e[j] -= hh * d[j];
	
					for (int j = 0; j < i; j++) 
					{
						f = d[j];
						g = e[j];
						for (int k = j; k <= i-1; k++)
							V[k,j] -= (f * e[k] + g * d[k]);
	
						d[j] = V[i-1,j];
						V[i,j] = 0.0;
					}
				}
				d[i] = h;
			}
		 
			// Accumulate transformations.
			for (int i = 0; i < n-1; i++) 
			{
				V[n-1,i] = V[i,i];
				V[i,i] = 1.0;
				double h = d[i+1];
				if (h != 0.0) 
				{
					for (int k = 0; k <= i; k++)
						d[k] = V[k,i+1] / h;
	
					for (int j = 0; j <= i; j++) 
					{
						double g = 0.0;
						for (int k = 0; k <= i; k++)
							g += V[k,i+1] * V[k,j];
						for (int k = 0; k <= i; k++)
							V[k,j] -= g * d[k];
					}
				}
		
				for (int k = 0; k <= i; k++)
					V[k,i+1] = 0.0;
			}
		
			for (int j = 0; j < n; j++) 
			{
				d[j] = V[n-1,j];
				V[n-1,j] = 0.0;
			}
				
			V[n-1,n-1] = 1.0;
			e[0] = 0.0;
		} 
		 
		private void tql2() 
		{
			// Symmetric tridiagonal QL algorithm.
			// This is derived from the Algol procedures tql2, by Bowdler, Martin, Reinsch, and Wilkinson, 
			// Handbook for Auto. Comp., Vol.ii-Linear Algebra, and the corresponding Fortran subroutine in EISPACK.
			for (int i = 1; i < n; i++)
				e[i-1] = e[i];
	
			e[n-1] = 0.0;
		 
			double f = 0.0;
			double tst1 = 0.0;
			double eps = Math.Pow(2.0,-52.0);
	
			for (int l = 0; l < n; l++) 
			{
				// Find small subdiagonal element.
				tst1 = Math.Max(tst1,Math.Abs(d[l]) + Math.Abs(e[l]));
				int m = l;
				while (m < n) 
				{
					if (Math.Abs(e[m]) <= eps*tst1)
						break;
					m++;
				}
		 
				// If m == l, d[l] is an eigenvalue, otherwise, iterate.
				if (m > l) 
				{
					int iter = 0;
					do 
					{
						iter = iter + 1;  // (Could check iteration count here.)
		 
						// Compute implicit shift
						double g = d[l];
						double p = (d[l+1] - g) / (2.0 * e[l]);
						double r = Hypotenuse(p,1.0);
						if (p < 0) 
						{
							r = -r;
						}
	
						d[l] = e[l] / (p + r);
						d[l+1] = e[l] * (p + r);
						double dl1 = d[l+1];
						double h = g - d[l];
						for (int i = l+2; i < n; i++) 
						{
							d[i] -= h;
						}

						f = f + h;
		 
						// Implicit QL transformation.
						p = d[m];
						double c = 1.0;
						double c2 = c;
						double c3 = c;
						double el1 = e[l+1];
						double s = 0.0;
						double s2 = 0.0;
						for (int i = m-1; i >= l; i--) 
						{
							c3 = c2;
							c2 = c;
							s2 = s;
							g = c * e[i];
							h = c * p;
							r = Hypotenuse(p,e[i]);
							e[i+1] = s * r;
							s = e[i] / r;
							c = p / r;
							p = c * d[i] - s * g;
							d[i+1] = h + s * (c * g + s * d[i]);
		 
							// Accumulate transformation.
							for (int k = 0; k < n; k++) 
							{
								h = V[k,i+1];
								V[k,i+1] = s * V[k,i] + c * h;
								V[k,i] = c * V[k,i] - s * h;
							}
						}
							
						p = -s * s2 * c3 * el1 * e[l] / dl1;
						e[l] = s * p;
						d[l] = c * p;
		 
						// Check for convergence.
					} 
					while (Math.Abs(e[l]) > eps*tst1);
				}
				d[l] = d[l] + f;
				e[l] = 0.0;
			}
			 
			// Sort eigenvalues and corresponding vectors.
			for (int i = 0; i < n-1; i++) 
			{
				int k = i;
				double p = d[i];
				for (int j = i+1; j < n; j++) 
				{
					if (d[j] < p) 
					{
						k = j;
						p = d[j];
					}
				}
					 
				if (k != i) 
				{
					d[k] = d[i];
					d[i] = p;
					for (int j = 0; j < n; j++) 
					{
						p = V[j,i];
						V[j,i] = V[j,k];
						V[j,k] = p;
					}
				}
			}
		}
		 
		private void orthes() 
		{
			// Nonsymmetric reduction to Hessenberg form.
			// This is derived from the Algol procedures orthes and ortran, by Martin and Wilkinson, 
			// Handbook for Auto. Comp., Vol.ii-Linear Algebra, and the corresponding Fortran subroutines in EISPACK.
			int low = 0;
			int high = n-1;
		 
			for (int m = low+1; m <= high-1; m++) 
			{
				// Scale column.
		 
				double scale = 0.0;
				for (int i = m; i <= high; i++)
					scale = scale + Math.Abs(H[i,m-1]);
	
				if (scale != 0.0) 
				{
					// Compute Householder transformation.
					double h = 0.0;
					for (int i = high; i >= m; i--) 
					{
						ort[i] = H[i,m-1]/scale;
						h += ort[i] * ort[i];
					}
						
					double g = Math.Sqrt(h);
					if (ort[m] > 0) g = -g;
	
					h = h - ort[m] * g;
					ort[m] = ort[m] - g;
		 
					// Apply Householder similarity transformation
					// H = (I - u * u' / h) * H * (I - u * u') / h)
					for (int j = m; j < n; j++) 
					{
						double f = 0.0;
						for (int i = high; i >= m; i--) 
							f += ort[i]*H[i,j];
	
						f = f/h;
						for (int i = m; i <= high; i++)
							H[i,j] -= f*ort[i];
					}
		 
					for (int i = 0; i <= high; i++) 
					{
						double f = 0.0;
						for (int j = high; j >= m; j--)
							f += ort[j]*H[i,j];
	
						f = f/h;
						for (int j = m; j <= high; j++)
							H[i,j] -= f*ort[j];
					}
	
					ort[m] = scale*ort[m];
					H[m,m-1] = scale*g;
				}
			}
		 
			// Accumulate transformations (Algol's ortran).
			for (int i = 0; i < n; i++)
				for (int j = 0; j < n; j++)
					V[i,j] = (i == j ? 1.0 : 0.0);
	
			for (int m = high-1; m >= low+1; m--) 
			{
				if (H[m,m-1] != 0.0) 
				{
					for (int i = m+1; i <= high; i++)
						ort[i] = H[i,m-1];
	
					for (int j = m; j <= high; j++) 
					{
						double g = 0.0;
						for (int i = m; i <= high; i++)
							g += ort[i] * V[i,j];
	
						// Double division avoids possible underflow.
						g = (g / ort[m]) / H[m,m-1];
						for (int i = m; i <= high; i++)
							V[i,j] += g * ort[i];
					}
				}
			}
		}
		 
		private void cdiv(double xr, double xi, double yr, double yi)
		{
			// Complex scalar division.
			double r;
			double d;
			if (Math.Abs(yr) > Math.Abs(yi)) 
			{
				r = yi/yr;
				d = yr + r*yi;
				cdivr = (xr + r*xi)/d;
				cdivi = (xi - r*xr)/d;
			} 
			else 
			{
				r = yr/yi;
				d = yi + r*yr;
				cdivr = (r*xr + xi)/d;
				cdivi = (r*xi - xr)/d;
			}
		}

		private void hqr2() 
		{
			// Nonsymmetric reduction from Hessenberg to real Schur form.   
			// This is derived from the Algol procedure hqr2, by Martin and Wilkinson, Handbook for Auto. Comp.,
			// Vol.ii-Linear Algebra, and the corresponding  Fortran subroutine in EISPACK.
			int nn = this.n;
			int n = nn-1;
			int low = 0;
			int high = nn-1;
			double eps = Math.Pow(2.0,-52.0);
			double exshift = 0.0;
			double p = 0;
			double q = 0;
			double r = 0;
			double s = 0;
			double z = 0;
			double t;
			double w;
			double x;
			double y;
		 
			// Store roots isolated by balanc and compute matrix norm
			double norm = 0.0;
			for (int i = 0; i < nn; i++) 
			{
				if (i < low | i > high) 
				{
					d[i] = H[i,i];
					e[i] = 0.0;
				}
					
				for (int j = Math.Max(i-1,0); j < nn; j++)
					norm = norm + Math.Abs(H[i,j]);
			}
		 
			// Outer loop over eigenvalue index
			int iter = 0;
			while (n >= low) 
			{
				// Look for single small sub-diagonal element
				int l = n;
				while (l > low) 
				{
					s = Math.Abs(H[l-1,l-1]) + Math.Abs(H[l,l]);
					if (s == 0.0) s = norm;
					if (Math.Abs(H[l,l-1]) < eps * s)
						break;
	
					l--;
				}
				 
				// Check for convergence
				if (l == n) 
				{
					// One root found
					H[n,n] = H[n,n] + exshift;
					d[n] = H[n,n];
					e[n] = 0.0;
					n--;
					iter = 0;
				} 
				else if (l == n-1) 
				{
					// Two roots found
					w = H[n,n-1] * H[n-1,n];
					p = (H[n-1,n-1] - H[n,n]) / 2.0;
					q = p * p + w;
					z = Math.Sqrt(Math.Abs(q));
					H[n,n] = H[n,n] + exshift;
					H[n-1,n-1] = H[n-1,n-1] + exshift;
					x = H[n,n];
		 
					if (q >= 0) 
					{
						// Real pair
						z = (p >= 0) ? (p + z) : (p - z);
						d[n-1] = x + z;
						d[n] = d[n-1];
						if (z != 0.0) 
							d[n] = x - w / z;
						e[n-1] = 0.0;
						e[n] = 0.0;
						x = H[n,n-1];
						s = Math.Abs(x) + Math.Abs(z);
						p = x / s;
						q = z / s;
						r = Math.Sqrt(p * p+q * q);
						p = p / r;
						q = q / r;
		 
						// Row modification
						for (int j = n-1; j < nn; j++) 
						{
							z = H[n-1,j];
							H[n-1,j] = q * z + p * H[n,j];
							H[n,j] = q * H[n,j] - p * z;
						}
			 
						// Column modification
						for (int i = 0; i <= n; i++) 
						{
							z = H[i,n-1];
							H[i,n-1] = q * z + p * H[i,n];
							H[i,n] = q * H[i,n] - p * z;
						}
			 
						// Accumulate transformations
						for (int i = low; i <= high; i++) 
						{
							z = V[i,n-1];
							V[i,n-1] = q * z + p * V[i,n];
							V[i,n] = q * V[i,n] - p * z;
						}
					}
					else 
					{
						// Complex pair
						d[n-1] = x + p;
						d[n] = x + p;
						e[n-1] = z;
						e[n] = -z;
					}
						
					n = n - 2;
					iter = 0;
				}
				else 
				{
					// No convergence yet	 
					
					// Form shift
					x = H[n,n];
					y = 0.0;
					w = 0.0;
					if (l < n) 
					{
						y = H[n-1,n-1];
						w = H[n,n-1] * H[n-1,n];
					}
		 
					// Wilkinson's original ad hoc shift
					if (iter == 10) 
					{
						exshift += x;
						for (int i = low; i <= n; i++)
							H[i,i] -= x;
	
						s = Math.Abs(H[n,n-1]) + Math.Abs(H[n-1,n-2]);
						x = y = 0.75 * s;
						w = -0.4375 * s * s;
					}
	
					// MATLAB's new ad hoc shift
					if (iter == 30) 
					{
						s = (y - x) / 2.0;
						s = s * s + w;
						if (s > 0) 
						{
							s = Math.Sqrt(s);
							if (y < x) s = -s;
							s = x - w / ((y - x) / 2.0 + s);
							for (int i = low; i <= n; i++)
								H[i,i] -= s;
							exshift += s;
							x = y = w = 0.964;
						}
					}
		 
					iter = iter + 1;
		 
					// Look for two consecutive small sub-diagonal elements
					int m = n-2;
					while (m >= l) 
					{
						z = H[m,m];
						r = x - z;
						s = y - z;
						p = (r * s - w) / H[m+1,m] + H[m,m+1];
						q = H[m+1,m+1] - z - r - s;
						r = H[m+2,m+1];
						s = Math.Abs(p) + Math.Abs(q) + Math.Abs(r);
						p = p / s;
						q = q / s;
						r = r / s;
						if (m == l) 
							break;
						if (Math.Abs(H[m,m-1]) * (Math.Abs(q) + Math.Abs(r)) < eps * (Math.Abs(p) * (Math.Abs(H[m-1,m-1]) + Math.Abs(z) +	Math.Abs(H[m+1,m+1])))) 
							break;
						m--;
					}
		 
					for (int i = m+2; i <= n; i++) 
					{
						H[i,i-2] = 0.0;
						if (i > m+2)
							H[i,i-3] = 0.0;
					}
		 
					// Double QR step involving rows l:n and columns m:n
					for (int k = m; k <= n-1; k++) 
					{
						bool notlast = (k != n-1);
						if (k != m) 
						{
							p = H[k,k-1];
							q = H[k+1,k-1];
							r = (notlast ? H[k+2,k-1] : 0.0);
							x = Math.Abs(p) + Math.Abs(q) + Math.Abs(r);
							if (x != 0.0) 
							{
								p = p / x;
								q = q / x;
								r = r / x;
							}
						}
							
						if (x == 0.0)	break;
	
						s = Math.Sqrt(p * p + q * q + r * r);
						if (p < 0) s = -s;
								 
						if (s != 0) 
						{
							if (k != m)
								H[k,k-1] = -s * x;
							else 
								if (l != m)
								H[k,k-1] = -H[k,k-1];
	
							p = p + s;
							x = p / s;
							y = q / s;
							z = r / s;
							q = q / p;
							r = r / p;
		 
							// Row modification
							for (int j = k; j < nn; j++) 
							{
								p = H[k,j] + q * H[k+1,j];
								if (notlast) 
								{
									p = p + r * H[k+2,j];
									H[k+2,j] = H[k+2,j] - p * z;
								}
								
								H[k,j] = H[k,j] - p * x;
								H[k+1,j] = H[k+1,j] - p * y;
							}
		 
							// Column modification
							for (int i = 0; i <= Math.Min(n,k+3); i++) 
							{
								p = x * H[i,k] + y * H[i,k+1];
								if (notlast) 
								{
									p = p + z * H[i,k+2];
									H[i,k+2] = H[i,k+2] - p * r;
								}
								
								H[i,k] = H[i,k] - p;
								H[i,k+1] = H[i,k+1] - p * q;
							}
		 
							// Accumulate transformations
							for (int i = low; i <= high; i++) 
							{
								p = x * V[i,k] + y * V[i,k+1];
								if (notlast) 
								{
									p = p + z * V[i,k+2];
									V[i,k+2] = V[i,k+2] - p * r;
								}
								
								V[i,k] = V[i,k] - p;
								V[i,k+1] = V[i,k+1] - p * q;
							}
						}
					}
				}
			}
				
			// Backsubstitute to find vectors of upper triangular form
			if (norm == 0.0) 
			{
				return;
			}
		 
			for (n = nn-1; n >= 0; n--) 
			{
				p = d[n];
				q = e[n];
		 
				// Real vector
				if (q == 0) 
				{
					int l = n;
					H[n,n] = 1.0;
					for (int i = n-1; i >= 0; i--) 
					{
						w = H[i,i] - p;
						r = 0.0;
						for (int j = l; j <= n; j++) 
							r = r + H[i,j] * H[j,n];
						
						if (e[i] < 0.0) 
						{
							z = w;
							s = r;
						}
						else 
						{
							l = i;
							if (e[i] == 0.0) 
							{
								H[i,n] = (w != 0.0) ? (-r / w) : (-r / (eps * norm));
							}
							else
							{
								// Solve real equations
								x = H[i,i+1];
								y = H[i+1,i];
								q = (d[i] - p) * (d[i] - p) + e[i] * e[i];
								t = (x * s - z * r) / q;
								H[i,n] = t;
								H[i+1,n] = (Math.Abs(x) > Math.Abs(z)) ? ((-r - w * t) / x) : ((-s - y * t) / z);
							}
		 
							// Overflow control
							t = Math.Abs(H[i,n]);
							if ((eps * t) * t > 1) 
								for (int j = i; j <= n; j++)
									H[j,n] = H[j,n] / t;
						}
					}
				}
				else if (q < 0) 
				{
					// Complex vector
					int l = n-1;
	
					// Last vector component imaginary so matrix is triangular
					if (Math.Abs(H[n,n-1]) > Math.Abs(H[n-1,n])) 
					{
						H[n-1,n-1] = q / H[n,n-1];
						H[n-1,n] = -(H[n,n] - p) / H[n,n-1];
					}
					else 
					{
						cdiv(0.0,-H[n-1,n],H[n-1,n-1]-p,q);
						H[n-1,n-1] = cdivr;
						H[n-1,n] = cdivi;
					}
						
					H[n,n-1] = 0.0;
					H[n,n] = 1.0;
					for (int i = n-2; i >= 0; i--) 
					{
						double ra,sa,vr,vi;
						ra = 0.0;
						sa = 0.0;
						for (int j = l; j <= n; j++) 
						{
							ra = ra + H[i,j] * H[j,n-1];
							sa = sa + H[i,j] * H[j,n];
						}
						
						w = H[i,i] - p;
		 
						if (e[i] < 0.0) 
						{
							z = w;
							r = ra;
							s = sa;
						}
						else 
						{
							l = i;
							if (e[i] == 0) 
							{
								cdiv(-ra,-sa,w,q);
								H[i,n-1] = cdivr;
								H[i,n] = cdivi;
							} 
							else 
							{
								// Solve complex equations
								x = H[i,i+1];
								y = H[i+1,i];
								vr = (d[i] - p) * (d[i] - p) + e[i] * e[i] - q * q;
								vi = (d[i] - p) * 2.0 * q;
								if (vr == 0.0 & vi == 0.0) 
									vr = eps * norm * (Math.Abs(w) + Math.Abs(q) + Math.Abs(x) + Math.Abs(y) + Math.Abs(z));
								cdiv(x*r-z*ra+q*sa,x*s-z*sa-q*ra,vr,vi);
								H[i,n-1] = cdivr;
								H[i,n] = cdivi;
								if (Math.Abs(x) > (Math.Abs(z) + Math.Abs(q))) 
								{
									H[i+1,n-1] = (-ra - w * H[i,n-1] + q * H[i,n]) / x;
									H[i+1,n] = (-sa - w * H[i,n] - q * H[i,n-1]) / x;
								}
								else 
								{
									cdiv(-r-y*H[i,n-1],-s-y*H[i,n],z,q);
									H[i+1,n-1] = cdivr;
									H[i+1,n] = cdivi;
								}
							}
		 
							// Overflow control
							t = Math.Max(Math.Abs(H[i,n-1]),Math.Abs(H[i,n]));
							if ((eps * t) * t > 1) 
								for (int j = i; j <= n; j++) 
								{
									H[j,n-1] = H[j,n-1] / t;
									H[j,n] = H[j,n] / t;
								}
						}
					}
				}
			}
		 
			// Vectors of isolated roots
			for (int i = 0; i < nn; i++) 
				if (i < low | i > high) 
					for (int j = i; j < nn; j++) 
						V[i,j] = H[i,j];
		 
			// Back transformation to get eigenvectors of original matrix
			for (int j = nn-1; j >= low; j--) 
				for (int i = low; i <= high; i++) 
				{
					z = 0.0;
					for (int k = low; k <= Math.Min(j,high); k++)
						z = z + V[i,k] * H[k,j];
					V[i,j] = z;
				}
		}

		/// <summary>Returns the real parts of the eigenvalues.</summary>
		public double[] RealEigenvalues
		{
			get 
			{ 
				return this.d; 
			}
		}
	
		/// <summary>Returns the imaginary parts of the eigenvalues.</summary>	
		public double[] ImaginaryEigenvalues
		{
			get 
			{ 
				return this.e; 
			}
		}

		/// <summary>Returns the eigenvector matrix.</summary>
		public Matrix EigenvectorMatrix
		{
			get 
			{ 
				return this.V; 
			}
		}
	
		/// <summary>Returns the block diagonal eigenvalue matrix.</summary>
		public Matrix DiagonalMatrix
		{
			get
			{
				Matrix X = new Matrix(n, n);
				double[][] x = X.Array;
	
				for (int i = 0; i < n; i++) 
				{
					for (int j = 0; j < n; j++)
						x[i][j] = 0.0;
	
					x[i][i] = d[i];
					if (e[i] > 0)
					{
						x[i][i+1] = e[i];
					}
					else if (e[i] < 0) 
					{
						x[i][i-1] = e[i];
					}
				}
				
				return X;
			}			
		}

		private static double Hypotenuse(double a, double b) 
		{
			if (Math.Abs(a) > Math.Abs(b))
			{
				double r = b / a;
				return Math.Abs(a) * Math.Sqrt(1 + r * r);
			}

			if (b != 0)
			{
				double r = a / b;
				return Math.Abs(b) * Math.Sqrt(1 + r * r);
			}

			return 0.0;
		}
	}
}
